多元动态演绎在Prover9证明器中的应用

Prover9证明器只采用二元归结方法,是一种静态的、局部的推理规则。基于矛盾体分离规则,提出了一种多元动态演绎算法,采用整体式演绎框架,通过子句演绎权重与文字演绎权重规划演绎路径,并带有回溯机制搜索较优路径。以CADE2017竞赛例(FOF组)进行测试,加入多元动态演绎算法的Prover9证明器证明定理总数提高了40.7%,且所用的平均时间降低了7.46 s。实验表明,提出的多元动态演绎算法是一种有效的推理方法,能有效提高一阶逻辑自动定理证明器的能力。     

数字趋势序列及其全序列匹配算法研究

针对基于点距离的时序数据分析和传统趋势序列分析的缺点,提出了数字趋势序列、序列的Lp距离、序列分段向量等概念,证明了包括“序列分段均值定理”在内的3个重要定理,设计了专门用于数字趋势序列的“基于序列分段向量（SSV）的全序列匹配算法”。算法使用片段斜率所对应的弧度值来度量片段的趋势,同时用趋势的保持时间来对趋势值进行加权,实现了数字趋势序列之间快速的全序列相似性搜索。     

Breadth-first search: Some surprising results

Although breadth-first search procedures cannot explore truly large search spaces, actual implementations of such procedures can result in surprisingly powerful problem-solvers that outperform more sophisticated heuristic search procedures. We describe two breadth-first search procedures. The first one, S&R, proves theorems from Principia of Whitehead and Russell, and is compared to two versions of the Logic Theorist. Previous estimates of the size of the search space are significantly reduced. When theorems are proved in an optimal order, this order differs markedly from that found in Principia, while more general theorems than those of Principia are often found.The second system, S&M, adapts breadth-first search to locally infinite search spaces in systems of rewriting rules. S&M is compared extensively to the heuristic theorem-prover of Quinlan and Hunt, and to some other theorem provers.     

目标可移动的直线搜索问题的在线算法研究

直线搜索问题也被叫做迷失的奶牛问题,解决这个问题的算法叫做线性螺旋搜索。该算法被证明是解决这个问题的最佳在线算法,它的竞争比是9。如果这个问题中的目标可以移动,那么这个问题就被强化了。本文将提出被强化后的问题的最佳在线算法及其竞争比。Minimax定理在这个算法中扮演着重要角色。     

Design Of Robust Pole Assignment Based On Pareto‐Optimal Solutions

In this paper, a new design method for robust pole assignment based on Pareto‐optimal solutions for an uncertain plant is proposed. The proposed design method is defined as a two‐objective optimization problem in which optimization of the settling time and damping ratio is translated into a pole assignment problem. The uncertainties of the plant are represented as a polytope of polynomials, and the design cost is reduced by using the edge theorem. The genetic algorithm is applied to optimize this problem because of its multiple search property. In order to demonstrate the effectiveness of the proposed design method, we applied the proposed design method to a magnetic levitation system.     

改进蚁群算法求解两地间时间最优路径

为提高蚁群算法的运算效率,提出一种改进的蚁群算法来求解问题。研究中中引入阀值排序算法对搜索路径进行优化,解决了蚁群算法前期搜索路径的盲目性问题。改进的蚁群算法加快了收敛速度,并提高了稳定性。经仿真试验证明,改进蚁群算法性在减少算法的迭代次数和提高解的稳定性方面有了较大的提高,并且能很好的用于求解路径时间最优问题。     

求解工件车间调度问题的一种新的邻域搜索算法

该文提出了一种新的求解工件车间调度(job shop scheduling)问题的邻域搜索算法．问题的目标是：在满足约束条件的前提下使得调度的makespan尽可能地小．定义了一种新的优先分配规则以生成初始解;定义了一种新的邻域结构;将邻域搜索跟单机调度结合在一起;提出了跳坑策略以跳出局部最优解并且将搜索引向有希望的方向．计算了当前国际文献中的一组共58个benchmark问题实例,算法的优度高于当前国外学者提出的两种著名的先进算法．其中对18个10工件10机器的实例,包括最著名的难解实例ft10,在可接受的时间内都找到了最优解．这些实例是当前文献中报导的所有规模为10工件10机器的实例．     

Linear fixed-point smoothing by using functional analysis

A new approach to the fixed-point smoothing problem for linear stochastic distributed parameter systems is proposed by using functional analysis. The number of sensor locations is assumed to be finite and the error criterion is based on the unbiased and least-squares estimations. The algorithm for an optimal fixed-point smoothing estimate is derived by using Itô's stochastic calculus in Hilbert spaces. By applying the kernel theorem to these results, a family of partial differential equations for the optimal fixed-point smoothing estimate is derived. The existence and uniqueness theorems concerning the solutions for both the smoothing gain and the smoothing estimator equations are proved. Finally, usefulness of the algorithm is illustrated with a numerical example.     

多项式等式型几何定理的可读证明

目前的智能几何软件都使用基于搜索法的定理证明器作为推理引擎,其主要缺点是不能可读地证明涉及到几何量代数运算的几何定理,这极大地限制了智能几何软件的实际应用.对一类结论为几何量多项式等式的几何定理,文中提出了一种能给出可读证明的启发式搜索算法.该算法通过引入多项式的变形操作算子——标准项代换,把证明结论为多项式等式g=0的几何定理转化为寻找从g到0的标准项代换序列的搜索问题.采用Lisp语言实现了该算法,并做了30个结论为几何量等式的几何定理的推理实验.实验结果表明算法具有较高的推理效率.     

Trade-off solutions in a single-machine scheduling problem for minimizing total earliness and maximum tardiness

This paper considers a single-machine scheduling problem involving minimization of the total earliness and the maximum tardiness. Four dominant properties for the precedence relationship between jobs in a search for an optimal solution are proposed. The lower bounds of the total earliness and the maximum tardiness of a subproblem are derived. The dominance properties and the lower bounds are implemented in the branchand-bound algorithm to facilitate the search for an optimal schedule. A heuristic algorithm is then developed to overcome the inefficiency of the branch-and-bound algorithm. Computational performance of the two algorithms is also investigated.     

一种求解二维矩形Packing问题的拟人型全局优化算法

针对二维矩形Packing问题,提出了基于占角动作的基本算法。以基本算法为基础,提出了三阶段优化的拟人型全局优化算法。在第一阶段生成初始布局。在第二阶段交替调用邻域搜索子程序和跳坑策略子程序对矩形块的优先级排序进行优化。邻域搜索采用交换式和插入式两种邻域结构,避免单一邻域结构的局限性。当搜索遇到局部最优解时,采用跳坑策略子程序跳出局部最优解,将搜索引向有希望的区域。在第三阶段调用优美度枚举子程序对占角动作的选择作进一步优化。提出了两条优度定理。对于六组benchmark测试用例的实验结果表明,算法的整体表现优于当前文献中的先进算法。针对矩形块方向固定的情形,算法对zdf6和zdf7两个问题实例得到了比已有文献记录更优的布局。     

并行机间歇过程生产调度的遗传局部搜索算法

研究了一类集成分批的并行机间歇过程调度问题(parallel machine batch process scheduling problem,简称PBPSP),将此问题转化为固定费用运输问题(6xed charge transportation problem,简称FCTP)后,提出了具有集中邻域搜索机制和局部最优逃逸机制的遗传局部搜索算法(genetic local search algorithm,简称GLSA).GLSA算法用先根遍历边排列模式编码生成树解,具有高效的子树补充式单点交叉操作.将基于网络单纯型方法的邻域搜索作为变异算子,并提出了连续随机节点邻域搜索的集中邻域搜索策略以及随机旋转变异与全局邻域搜索相结合的局部最优逃逸策略,极大地强化了遗传局部搜索算法的全局寻优能力.实验表明:GLSA算法获得的解质量优于基于排列编码的遗传算法和基于矩阵编码的遗传算法,得到了所有Benchmark问题的最优解,且具有高鲁棒性.针对一定规模的FCTP问题,GLSA算法比Tabu启发式搜索算法具有更高的获得最优解几率.     

Time and cost tradeoff for distributed data processing

An important design issue in distributed data processing systems is to determine optimal data distribution. The problem requires a tradeoff between time and cost. For instance, quick response time conflicts with low cost. The paper addresses the data distribution problem in this conflicting environment. A formulation of the problem as a non-linear program is developed. An algorithm employing a simple search procedure is presented, which gives an optimal data distribution. An example is solved to illustrate the method.     

An Enhanced tabu search algorithm to minimize a bi-criteria objective in batching and scheduling problems on unrelated-parallel machines with desired lower bounds on batch sizes

This paper addresses a sequence- and machine-dependent batch scheduling problem on a set of unrelated-parallel machines where the objective is to minimize a linear combination of total weighted completion time and total weighted tardiness. In particular, batch scheduling disregards the group technology assumptions by allowing for the possibility of splitting pre-determined groups of jobs into batches with respect to desired lower bounds on batch sizes. With regard to bounds on batch sizes, the MILP model is developed as two integrated batching and scheduling phases to present the problem. A benchmark of small-size instances on group scheduling shows the superior performance of batch scheduling up to 37% reduction in the objective function value. An efficient meta-heuristic algorithm based on tabu search with multi-level diversification and multi-tabu structure is developed at three levels, which moves back and forth between batching and scheduling phases. To eliminate searching in ineffective neighborhoods and thus enhance computational efficiency of search algorithms, several lemmas are proposed and proven. The results of applying lemmas reflect up to 40% reduction in computational times. Comparing the optimal solutions found by CPLEX and tabu search shows that the tabu search algorithm could find solutions, at least as good as CPLEX but in incredibly shorter computational time. In order to trigger the search algorithm, two different initial solution finding mechanisms have been developed and implemented. Also, due to lack of a qualified benchmark for unrelated-parallel machines, a comprehensive data generation mechanism has been developed in a way that it fairly reflects the real world situations encountered in practice. The machine availability times and job release times are considered to be dynamic and the run time of each job differs on different machines based upon the capability of the machines.     

Theorems on multidimensional laplace transform for solution of boundary value problems

Boundary value problems in two or more variables characterized by partial differential equations can be solved by a direct use of multidimensional Laplace transform. The general theory for obtaining solutions in this technique is developed in this paper by providing theorems on Laplace transform in n dimensions. Examples are presented for each theorem. Once the basic theorems are established it is possible to derive many useful transform pairs in n variables. Use of the above technique is illustrated by solution of an electrostatic potential problem.     

求最优装载的量子算法

随着Grover量子搜索算法的不断发展,它的实际应用价值也在逐渐体现.通过介绍量子并行计算和量子算法的基本思想以及对改进的Grover搜索算法进行研究的基础上,分析给出了一个时间复杂度为O(√N)的求解最优装载问题的量子算法.对于最优装载问题,分别用经典计算机上的贪心算法和量子算法来求解,得出了这两种算法的时间复杂度,从而可以看出量子算法相对于经典算法具有更快的搜索速度.     

极小化加权完工时间的多资源工序的资源分配问题

针对现实中广泛存在的多资源工序的资源分配问题,考虑基于资源使用的优先次序约束,以最小化加权完工时间为优化目标,构建一类新的资源分配混合整数线性规划模型.其次,提出Benders分解和禁忌搜索的混合算法,该混合算法以Benders分解为基本框架,将原问题分为提供资源分配方案的主问题和计算工序加权完工时间的子问题,并通过改进数学模型和添加禁忌搜索提高混合算法的收敛速度.最后,通过300个随机仿真算例测试结果表明,在相同时间下求解小规模问题时,所提的Benders分解混合算法能获得距离商业求解器CPLEX最优解平均差距为0.86%的满意解;在求解大规模问题时,所提出的算法的性能表现优于CPLEX、禁忌搜索算法、变邻域搜索算法和Benders分解嵌入遗传算法的混合方法,能给出更好的资源分配方案,与CPLEX相比,上界和下界分别改善了4.74%和9.62%.     

基于不相关属性集合的属性探索算法

作为形式概念分析理论中的一个重要工具,属性探索算法能够以问题为导向,交互式地逐步发现系统知识,在知识的发现和获取中居于核心地位。但是,当形式背景的规模较大时,属性探索算法的计算过程过于耗时,严重制约了算法在当前大数据时代的推广与应用。耗时瓶颈主要存在于“寻找下一个与专家交互的问题”这一环节,传统算法在此过程中存在大量冗余计算。针对这个问题,在分析伪内涵和内涵与蕴涵集合的内在逻辑关系的基础上,提出并证明了3个定理,根据定理给出了一种基于不相关属性集合的属性探索算法,该算法在计算伪内涵与内涵的过程中,借助提出的定理,跳过违反该逻辑关系的属性集合是否为伪内涵或者内涵的判断过程,减小了算法的搜索空间,从而降低了算法的时间复杂度。所提算法最好的时间复杂度为O(mn²P²),最坏的时间复杂度为O(mn³P²)。实验结果表明,与传统算法相比,该算法具有较为明显的时间性能优势。     

求解带容量和时间窗约束车辆路径问题的改进蝙蝠算法

带时间窗和容量约束的车辆路径问题是车辆路径问题重要的扩展之一,属于NP难题,精确算法的求解效率较低,且对于较大规模问题难以在有限时间内给出最优解.为了满足企业和客户快速有效的配送需求,使用智能优化算法可以在有限的时间内给出相对较优解.研究了求解带容量和时间窗约束车辆路径问题的改进离散蝙蝠算法,为增加扰动机制,提高搜索速度和精度,在对客户点按其所在位置进行聚类的基础上,在算法中引入了变步长搜索策略和两元素优化方法进行局部搜索.仿真实验结果表明,所设计算法具有较高寻优能力和较强的实用价值.     

Assignment and scheduling communicating periodic tasks indistributed real-time systems

Presents an optimal solution to the problem of allocating communicating periodic tasks to heterogeneous processing nodes (PNs) in a distributed real-time system. The solution is optimal in the sense of minimizing the maximum normalized task response time, called the system hazard, subject to the precedence constraints resulting from intercommunication among the tasks to be allocated. Minimization of the system hazard ensures that the solution algorithm allocates tasks so as to meet all task deadlines under an optimal schedule, whenever such an allocation exists. The task system is modeled with a task graph (TG), in which computation and communication modules, communication delays and intertask precedence constraints are clearly described. Tasks described by this TG are assigned to PNs by using a branch-and-bound (B&B) search algorithm. The algorithm traverses a search tree whose leaves correspond to potential solutions to the task allocation problem. We use a bounding method that prunes, in polynomial time, nonleaf vertices that cannot lead to an optimal solution, while ensuring that the search path leading to an optimal solution will never be pruned. For each generated leaf vertex, we compute the exact cost using the algorithm developed by Peng and Shin (1993). The lowest-cost leaf vertex (one with the least system hazard) represents an optimal task allocation. Computational experiences and examples are provided to demonstrate the concept, utility and power of the proposed approach